He claims to have an argument that P=NP. He’s a philosopher, so “argument” != proof. Although approaching P=NP as a philosophical argument does strike me as kooky.
If it’s this argument, it’s wrong. It is based on the claim that soap films solve the Steiner problem, which they don’t. I tried this myself for four pins; here is a report of six-pin soap-film configurations. The soap film, obviously, only finds a local minimum, not a global one. But finding a local minimum is computationally easy.
Elsewhere, in a paper that detracts from the credibility of the journal it appears in, he argues that people can perform hypercomputation, on the grounds that we can imagine people performing hypercomputation. (Yes, I read all 24 pages, and that’s what it comes down to.)
One element of his argument was that proofs using hyperset logic (which he said is an entire field of logic nowadays; I wouldn’t know)
Judging by Google, the only wide use of the word “hyperset” in mathematics is in non-well-founded set theory. If that is what he was talking about, it’s equiconsistent with the usual sort of set theory and has no more significance for AI than the choice of programming language (which, in my view, has no significance for AI).
What is it with AI? Does it attract the insane, or does it drive them insane? ETA: Or attract the people that it can drive insane?
Oh… This is sad work (Bringsjord). His argument for hypercomputation by people seems remarkably similar to Alvin Plantinga’s Modal Ontological Argument for God.
I am also suspect of much of what Penrose has to say about Computationalism, although I am not yet sufficiently knowledgeable to be able to directly confront his work in any meaningful way (I am working to rectify that problem. I seem to have a knack for formal logic, and I am hoping that when I get to upper division logic classes that I will be able to more directly confront arguments like Penrose’s and Bringsjord’s)
If it’s this argument, it’s wrong. It is based on the claim that soap films solve the Steiner problem, which they don’t. I tried this myself for four pins; here is a report of six-pin soap-film configurations. The soap film, obviously, only finds a local minimum, not a global one. But finding a local minimum is computationally easy.
Elsewhere, in a paper that detracts from the credibility of the journal it appears in, he argues that people can perform hypercomputation, on the grounds that we can imagine people performing hypercomputation. (Yes, I read all 24 pages, and that’s what it comes down to.)
Judging by Google, the only wide use of the word “hyperset” in mathematics is in non-well-founded set theory. If that is what he was talking about, it’s equiconsistent with the usual sort of set theory and has no more significance for AI than the choice of programming language (which, in my view, has no significance for AI).
What is it with AI? Does it attract the insane, or does it drive them insane? ETA: Or attract the people that it can drive insane?
Oh… This is sad work (Bringsjord). His argument for hypercomputation by people seems remarkably similar to Alvin Plantinga’s Modal Ontological Argument for God.
I am also suspect of much of what Penrose has to say about Computationalism, although I am not yet sufficiently knowledgeable to be able to directly confront his work in any meaningful way (I am working to rectify that problem. I seem to have a knack for formal logic, and I am hoping that when I get to upper division logic classes that I will be able to more directly confront arguments like Penrose’s and Bringsjord’s)